The given equation is a quadratic equation:

$x^2 + 9x - 10 = 0$

We can solve this using the quadratic formula, which is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For the given equation $x^2 + 9x - 10 = 0$, the coefficients are:

• $a = 1$
• $b = 9$
• $c = -10$

Substitute these values into the quadratic formula:

$x = \frac{-9 \pm \sqrt{9^2 - 4(1)(-10)}}{2(1)}$

$x = \frac{-9 \pm \sqrt{81 + 40}}{2}$

$x = \frac{-9 \pm \sqrt{121}}{2}$

$x = \frac{-9 \pm 11}{2}$

Now, calculate the two possible solutions:

1. $x = \frac{-9 + 11}{2} = \frac{2}{2} = 1$
2. $x = \frac{-9 - 11}{2} = \frac{-20}{2} = -10$

Thus, the solutions are:

$x = 1 \quad \text{or} \quad x = -10$

Would you like more details or have any questions?

Here are some related questions:

1. How can you verify the solutions to a quadratic equation?
2. What are other methods to solve quadratic equations?
3. What is the discriminant, and how is it used in the quadratic formula?
4. How do you factor a quadratic equation?
5. What are real-world applications of quadratic equations?

Tip: Always check the discriminant ($b^2 - 4ac$) to know if the quadratic equation has real or complex solutions.